The CSS property ‘line-height’ actually accepts a pure numerical value, which will work out the line height based on the font size set. If you want to use the golden ratio (1.61803399), then you could set this as the line height in the body.
body {
font: 100%/1.618 sans-serif;
}
As an example, setting a H1’s font-size to 24px would produce a line-height of 39px (rounded up from 38.832).